From e9bac094277fc3f06445d6e2bff7c810343289b9 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Thu, 31 Aug 2023 06:13:22 +0200
Subject: [PATCH] small typos

---
 doc/pub/week35/html/._week35-bs057.html      |   2 +-
 doc/pub/week35/html/._week35-bs058.html      |   2 +-
 doc/pub/week35/html/week35-reveal.html       |   4 +-
 doc/pub/week35/html/week35-solarized.html    |   4 +-
 doc/pub/week35/html/week35.html              |   4 +-
 doc/pub/week35/ipynb/ipynb-week35-src.tar.gz | Bin 191 -> 191 bytes
 doc/pub/week35/ipynb/week35.ipynb            | 860 +++++++++----------
 doc/src/week35/week35.do.txt                 |   4 +-
 8 files changed, 440 insertions(+), 440 deletions(-)

diff --git a/doc/pub/week35/html/._week35-bs057.html b/doc/pub/week35/html/._week35-bs057.html
index 5c4bde9f6..047b36e1e 100644
--- a/doc/pub/week35/html/._week35-bs057.html
+++ b/doc/pub/week35/html/._week35-bs057.html
@@ -377,7 +377,7 @@ function, that is we have
 </p>
 
 $$
-\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
+\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
 $$
 
 <p>This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).</p>
diff --git a/doc/pub/week35/html/._week35-bs058.html b/doc/pub/week35/html/._week35-bs058.html
index f52640fb5..b6bab24dc 100644
--- a/doc/pub/week35/html/._week35-bs058.html
+++ b/doc/pub/week35/html/._week35-bs058.html
@@ -405,7 +405,7 @@ with a factor \( 1/(n-1) \). This is called <a href="https://mathworld.wolfram.c
 method corrects the bias in the estimation of the population variance
 and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
-<b>Scikit-Learn</b> or <b>nunmpy's</b> function calculate the covariance, this
+<b>Scikit-Learn</b> or <b>nunmpy's</b> function to calculate the covariance, this
 quantity will be computed with a factor \( 1/(n-1) \).
 </p>
 
diff --git a/doc/pub/week35/html/week35-reveal.html b/doc/pub/week35/html/week35-reveal.html
index ac7e175af..73bc276b6 100644
--- a/doc/pub/week35/html/week35-reveal.html
+++ b/doc/pub/week35/html/week35-reveal.html
@@ -2950,7 +2950,7 @@ function, that is we have
 
 <p>&nbsp;<br>
 $$
-\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
+\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
 $$
 <p>&nbsp;<br>
 
@@ -3018,7 +3018,7 @@ with a factor \( 1/(n-1) \). This is called <a href="https://mathworld.wolfram.c
 method corrects the bias in the estimation of the population variance
 and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
-<b>Scikit-Learn</b> or <b>nunmpy's</b> function calculate the covariance, this
+<b>Scikit-Learn</b> or <b>nunmpy's</b> function to calculate the covariance, this
 quantity will be computed with a factor \( 1/(n-1) \).
 </p>
 </section>
diff --git a/doc/pub/week35/html/week35-solarized.html b/doc/pub/week35/html/week35-solarized.html
index 43267a8e9..0f1fa52af 100644
--- a/doc/pub/week35/html/week35-solarized.html
+++ b/doc/pub/week35/html/week35-solarized.html
@@ -2823,7 +2823,7 @@ function, that is we have
 </p>
 
 $$
-\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
+\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
 $$
 
 <p>This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).</p>
@@ -2879,7 +2879,7 @@ with a factor \( 1/(n-1) \). This is called <a href="https://mathworld.wolfram.c
 method corrects the bias in the estimation of the population variance
 and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
-<b>Scikit-Learn</b> or <b>nunmpy's</b> function calculate the covariance, this
+<b>Scikit-Learn</b> or <b>nunmpy's</b> function to calculate the covariance, this
 quantity will be computed with a factor \( 1/(n-1) \).
 </p>
 
diff --git a/doc/pub/week35/html/week35.html b/doc/pub/week35/html/week35.html
index 837abce5a..f959be984 100644
--- a/doc/pub/week35/html/week35.html
+++ b/doc/pub/week35/html/week35.html
@@ -2900,7 +2900,7 @@ function, that is we have
 </p>
 
 $$
-\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}^T\partial \boldsymbol{\beta}} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
+\frac{\partial^2 C(\boldsymbol{\beta})}{\partial \boldsymbol{\beta}\partial \boldsymbol{\beta}^T} =\frac{2}{n}\boldsymbol{X}^T\boldsymbol{X}.  
 $$
 
 <p>This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).</p>
@@ -2956,7 +2956,7 @@ with a factor \( 1/(n-1) \). This is called <a href="https://mathworld.wolfram.c
 method corrects the bias in the estimation of the population variance
 and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
-<b>Scikit-Learn</b> or <b>nunmpy's</b> function calculate the covariance, this
+<b>Scikit-Learn</b> or <b>nunmpy's</b> function to calculate the covariance, this
 quantity will be computed with a factor \( 1/(n-1) \).
 </p>
 
diff --git a/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz b/doc/pub/week35/ipynb/ipynb-week35-src.tar.gz
index 6d899cd1864df13805929656c2a04890f610b4f7..75552ed8f53cb5dc116f18a7f25bb4b9f6777d1d 100644
GIT binary patch
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diff --git a/doc/pub/week35/ipynb/week35.ipynb b/doc/pub/week35/ipynb/week35.ipynb
index baa97aaf4..6c23bf707 100644
--- a/doc/pub/week35/ipynb/week35.ipynb
+++ b/doc/pub/week35/ipynb/week35.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
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-   "id": "7577bda1",
+   "id": "be53b5a0",
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@@ -14,7 +14,7 @@
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-   "id": "2f58994e",
+   "id": "ea9aa8ba",
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@@ -27,7 +27,7 @@
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+   "id": "1682c283",
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@@ -49,7 +49,7 @@
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@@ -65,7 +65,7 @@
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@@ -99,7 +99,7 @@
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+   "id": "94c25631",
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@@ -115,7 +115,7 @@
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+   "id": "a42b88dc",
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@@ -127,7 +127,7 @@
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+   "id": "3171d71c",
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@@ -137,7 +137,7 @@
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+   "id": "e70f9acc",
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@@ -149,7 +149,7 @@
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@@ -170,7 +170,7 @@
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+   "id": "643717b0",
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@@ -182,7 +182,7 @@
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+   "id": "378c280f",
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@@ -195,7 +195,7 @@
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+   "id": "e52a2672",
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@@ -207,7 +207,7 @@
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-   "id": "b8e38e10",
+   "id": "cce68c3d",
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@@ -219,7 +219,7 @@
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+   "id": "f8c11724",
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@@ -229,7 +229,7 @@
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+   "id": "a139ab45",
    "metadata": {
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@@ -241,7 +241,7 @@
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-   "id": "8ba76773",
+   "id": "089dec59",
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@@ -254,7 +254,7 @@
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+   "id": "570e9155",
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@@ -266,7 +266,7 @@
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-   "id": "b6562367",
+   "id": "2c6cbd01",
    "metadata": {
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@@ -276,7 +276,7 @@
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+   "id": "daaf53c3",
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@@ -288,7 +288,7 @@
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-   "id": "a0a15628",
+   "id": "186a0c23",
    "metadata": {
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@@ -300,7 +300,7 @@
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-   "id": "ad1e37fe",
+   "id": "e83c76fe",
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@@ -311,7 +311,7 @@
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-   "id": "bfc33b62",
+   "id": "48869faa",
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@@ -323,7 +323,7 @@
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-   "id": "05d1562e",
+   "id": "09ef84bc",
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@@ -342,7 +342,7 @@
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+   "id": "a3573593",
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@@ -355,7 +355,7 @@
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+   "id": "0cf80555",
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@@ -365,7 +365,7 @@
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+   "id": "9a5943d2",
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@@ -377,7 +377,7 @@
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-   "id": "c9d3f7d2",
+   "id": "614492f6",
    "metadata": {
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@@ -387,7 +387,7 @@
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+   "id": "e151cfa1",
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@@ -399,7 +399,7 @@
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@@ -409,7 +409,7 @@
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+   "id": "62ea2b3f",
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@@ -421,7 +421,7 @@
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@@ -432,7 +432,7 @@
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@@ -444,7 +444,7 @@
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@@ -454,7 +454,7 @@
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+   "id": "d80df328",
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@@ -466,7 +466,7 @@
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@@ -476,7 +476,7 @@
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@@ -488,7 +488,7 @@
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@@ -508,7 +508,7 @@
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@@ -535,7 +535,7 @@
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@@ -547,7 +547,7 @@
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@@ -559,7 +559,7 @@
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@@ -575,7 +575,7 @@
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@@ -605,7 +605,7 @@
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@@ -628,7 +628,7 @@
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@@ -640,7 +640,7 @@
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@@ -650,7 +650,7 @@
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@@ -662,7 +662,7 @@
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@@ -688,7 +688,7 @@
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@@ -700,7 +700,7 @@
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@@ -712,7 +712,7 @@
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@@ -722,7 +722,7 @@
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@@ -734,7 +734,7 @@
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@@ -746,7 +746,7 @@
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@@ -772,7 +772,7 @@
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@@ -808,7 +808,7 @@
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@@ -818,7 +818,7 @@
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@@ -830,7 +830,7 @@
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@@ -840,7 +840,7 @@
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@@ -852,7 +852,7 @@
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@@ -862,7 +862,7 @@
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@@ -886,7 +886,7 @@
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@@ -898,7 +898,7 @@
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@@ -913,7 +913,7 @@
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@@ -925,7 +925,7 @@
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@@ -935,7 +935,7 @@
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@@ -947,7 +947,7 @@
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@@ -957,7 +957,7 @@
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@@ -969,7 +969,7 @@
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@@ -979,7 +979,7 @@
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@@ -991,7 +991,7 @@
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@@ -1003,7 +1003,7 @@
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@@ -1015,7 +1015,7 @@
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@@ -1025,7 +1025,7 @@
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@@ -1037,7 +1037,7 @@
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@@ -1050,7 +1050,7 @@
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@@ -1062,7 +1062,7 @@
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@@ -1072,7 +1072,7 @@
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@@ -1084,7 +1084,7 @@
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@@ -1094,7 +1094,7 @@
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@@ -1106,7 +1106,7 @@
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@@ -1116,7 +1116,7 @@
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@@ -1128,7 +1128,7 @@
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@@ -1138,7 +1138,7 @@
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@@ -1150,7 +1150,7 @@
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@@ -1160,7 +1160,7 @@
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@@ -1172,7 +1172,7 @@
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@@ -1184,7 +1184,7 @@
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@@ -1196,7 +1196,7 @@
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@@ -1208,7 +1208,7 @@
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@@ -1220,7 +1220,7 @@
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@@ -1236,7 +1236,7 @@
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@@ -1248,7 +1248,7 @@
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@@ -1258,7 +1258,7 @@
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@@ -1270,7 +1270,7 @@
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@@ -1288,7 +1288,7 @@
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@@ -1300,7 +1300,7 @@
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@@ -1312,7 +1312,7 @@
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@@ -1322,7 +1322,7 @@
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@@ -1334,7 +1334,7 @@
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@@ -1344,7 +1344,7 @@
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@@ -1356,7 +1356,7 @@
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@@ -1366,7 +1366,7 @@
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@@ -1380,7 +1380,7 @@
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@@ -1392,7 +1392,7 @@
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@@ -1403,7 +1403,7 @@
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@@ -1416,7 +1416,7 @@
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@@ -1443,7 +1443,7 @@
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@@ -1454,7 +1454,7 @@
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@@ -1467,7 +1467,7 @@
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@@ -1481,7 +1481,7 @@
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@@ -1494,7 +1494,7 @@
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@@ -1505,7 +1505,7 @@
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@@ -1517,7 +1517,7 @@
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@@ -1528,7 +1528,7 @@
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@@ -1544,7 +1544,7 @@
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@@ -1555,7 +1555,7 @@
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@@ -1569,7 +1569,7 @@
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@@ -1590,7 +1590,7 @@
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@@ -1601,7 +1601,7 @@
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@@ -1654,7 +1654,7 @@
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@@ -1665,7 +1665,7 @@
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@@ -1690,7 +1690,7 @@
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@@ -1702,7 +1702,7 @@
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@@ -1731,7 +1731,7 @@
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@@ -1756,7 +1756,7 @@
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@@ -1776,7 +1776,7 @@
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@@ -1803,7 +1803,7 @@
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@@ -1816,7 +1816,7 @@
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@@ -1828,7 +1828,7 @@
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@@ -1839,7 +1839,7 @@
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@@ -1855,7 +1855,7 @@
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@@ -1889,7 +1889,7 @@
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@@ -1899,7 +1899,7 @@
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@@ -1914,7 +1914,7 @@
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@@ -1926,7 +1926,7 @@
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@@ -1936,7 +1936,7 @@
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@@ -1952,7 +1952,7 @@
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@@ -1969,7 +1969,7 @@
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@@ -1982,7 +1982,7 @@
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@@ -2029,7 +2029,7 @@
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@@ -2040,7 +2040,7 @@
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@@ -2143,7 +2143,7 @@
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@@ -2171,7 +2171,7 @@
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@@ -2206,7 +2206,7 @@
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@@ -2221,7 +2221,7 @@
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@@ -2246,7 +2246,7 @@
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@@ -2262,7 +2262,7 @@
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@@ -2274,7 +2274,7 @@
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@@ -2289,7 +2289,7 @@
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@@ -2301,7 +2301,7 @@
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@@ -2311,7 +2311,7 @@
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@@ -2323,7 +2323,7 @@
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@@ -2333,7 +2333,7 @@
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@@ -2345,7 +2345,7 @@
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@@ -2358,7 +2358,7 @@
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@@ -2370,7 +2370,7 @@
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@@ -2380,7 +2380,7 @@
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@@ -2392,7 +2392,7 @@
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@@ -2402,7 +2402,7 @@
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@@ -2414,7 +2414,7 @@
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@@ -2424,7 +2424,7 @@
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@@ -2436,7 +2436,7 @@
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@@ -2446,7 +2446,7 @@
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@@ -2458,7 +2458,7 @@
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@@ -2468,7 +2468,7 @@
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@@ -2480,7 +2480,7 @@
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@@ -2490,7 +2490,7 @@
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@@ -2502,7 +2502,7 @@
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@@ -2514,7 +2514,7 @@
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@@ -2526,7 +2526,7 @@
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@@ -2539,7 +2539,7 @@
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@@ -2551,7 +2551,7 @@
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@@ -2561,7 +2561,7 @@
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@@ -2575,7 +2575,7 @@
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@@ -2672,7 +2672,7 @@
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@@ -2693,7 +2693,7 @@
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@@ -2705,7 +2705,7 @@
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@@ -2715,7 +2715,7 @@
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@@ -2727,7 +2727,7 @@
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@@ -2737,7 +2737,7 @@
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@@ -2749,7 +2749,7 @@
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@@ -2765,7 +2765,7 @@
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@@ -2809,7 +2809,7 @@
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@@ -2821,7 +2821,7 @@
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@@ -2837,7 +2837,7 @@
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@@ -2848,7 +2848,7 @@
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@@ -2866,7 +2866,7 @@
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@@ -2877,7 +2877,7 @@
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@@ -2891,7 +2891,7 @@
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@@ -2902,7 +2902,7 @@
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@@ -2915,7 +2915,7 @@
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@@ -2926,7 +2926,7 @@
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@@ -2943,7 +2943,7 @@
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@@ -2954,7 +2954,7 @@
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@@ -2970,7 +2970,7 @@
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@@ -2981,7 +2981,7 @@
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@@ -3005,7 +3005,7 @@
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@@ -3016,7 +3016,7 @@
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@@ -3029,7 +3029,7 @@
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@@ -3040,7 +3040,7 @@
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@@ -3060,7 +3060,7 @@
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@@ -3071,7 +3071,7 @@
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@@ -3114,7 +3114,7 @@
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@@ -3129,7 +3129,7 @@
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@@ -3139,7 +3139,7 @@
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@@ -3153,7 +3153,7 @@
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@@ -3165,7 +3165,7 @@
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@@ -3177,7 +3177,7 @@
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@@ -3189,7 +3189,7 @@
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@@ -3199,7 +3199,7 @@
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@@ -3211,7 +3211,7 @@
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@@ -3221,7 +3221,7 @@
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@@ -3233,7 +3233,7 @@
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@@ -3244,7 +3244,7 @@
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@@ -3256,7 +3256,7 @@
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@@ -3268,7 +3268,7 @@
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@@ -3278,7 +3278,7 @@
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@@ -3290,7 +3290,7 @@
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@@ -3302,7 +3302,7 @@
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@@ -3312,7 +3312,7 @@
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@@ -3324,7 +3324,7 @@
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@@ -3334,7 +3334,7 @@
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@@ -3346,7 +3346,7 @@
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@@ -3356,7 +3356,7 @@
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@@ -3396,7 +3396,7 @@
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@@ -3413,7 +3413,7 @@
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@@ -3436,7 +3436,7 @@
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@@ -3453,7 +3453,7 @@
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@@ -3472,7 +3472,7 @@
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@@ -3483,7 +3483,7 @@
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@@ -3495,7 +3495,7 @@
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@@ -3513,7 +3513,7 @@
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@@ -3529,7 +3529,7 @@
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@@ -3541,7 +3541,7 @@
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@@ -3551,7 +3551,7 @@
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@@ -3566,7 +3566,7 @@
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@@ -3578,7 +3578,7 @@
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@@ -3588,7 +3588,7 @@
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@@ -3600,7 +3600,7 @@
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@@ -3610,7 +3610,7 @@
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@@ -3622,7 +3622,7 @@
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@@ -3634,7 +3634,7 @@
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@@ -3649,7 +3649,7 @@
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@@ -3660,7 +3660,7 @@
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@@ -3680,7 +3680,7 @@
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@@ -3692,7 +3692,7 @@
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@@ -3702,7 +3702,7 @@
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@@ -3714,7 +3714,7 @@
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@@ -3743,7 +3743,7 @@
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@@ -3770,7 +3770,7 @@
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@@ -3781,7 +3781,7 @@
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@@ -3821,7 +3821,7 @@
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@@ -3838,7 +3838,7 @@
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@@ -3861,7 +3861,7 @@
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@@ -3875,7 +3875,7 @@
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@@ -3894,7 +3894,7 @@
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@@ -3904,7 +3904,7 @@
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@@ -3916,7 +3916,7 @@
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@@ -3930,7 +3930,7 @@
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@@ -3942,7 +3942,7 @@
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@@ -3952,7 +3952,7 @@
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@@ -3964,7 +3964,7 @@
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-   "id": "bdc865ea",
+   "id": "f70d6ea7",
    "metadata": {
     "editable": true
    },
@@ -3981,7 +3981,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6560516f",
+   "id": "68ecbbfa",
    "metadata": {
     "editable": true
    },
@@ -3991,7 +3991,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0913014f",
+   "id": "73db495d",
    "metadata": {
     "editable": true
    },
@@ -4007,7 +4007,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7960d3eb",
+   "id": "44412861",
    "metadata": {
     "editable": true
    },
@@ -4017,7 +4017,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2c6cab1",
+   "id": "985de8ad",
    "metadata": {
     "editable": true
    },
@@ -4033,7 +4033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d026c4fa",
+   "id": "bae93d68",
    "metadata": {
     "editable": true
    },
@@ -4043,7 +4043,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc5999f4",
+   "id": "e29bd644",
    "metadata": {
     "editable": true
    },
@@ -4059,7 +4059,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1753c718",
+   "id": "3abf4a2d",
    "metadata": {
     "editable": true
    },
@@ -4069,7 +4069,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb1ffbac",
+   "id": "fe1e2ce7",
    "metadata": {
     "editable": true
    },
@@ -4086,7 +4086,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9d5ba9ce",
+   "id": "d23d044b",
    "metadata": {
     "editable": true
    },
@@ -4098,7 +4098,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fc09fc11",
+   "id": "36e38f22",
    "metadata": {
     "editable": true
    },
@@ -4110,7 +4110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36822227",
+   "id": "ad22843b",
    "metadata": {
     "editable": true
    },
@@ -4122,7 +4122,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "de6cc474",
+   "id": "fabcf0f8",
    "metadata": {
     "editable": true
    },
@@ -4132,7 +4132,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "453ff6f8",
+   "id": "2c2f44c5",
    "metadata": {
     "editable": true
    },
@@ -4144,7 +4144,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fb1165b",
+   "id": "105762d0",
    "metadata": {
     "editable": true
    },
@@ -4156,7 +4156,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb0b59b1",
+   "id": "35a42e41",
    "metadata": {
     "editable": true
    },
@@ -4168,7 +4168,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1c998fc7",
+   "id": "8e21698f",
    "metadata": {
     "editable": true
    },
@@ -4178,7 +4178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b91e913",
+   "id": "a240efc0",
    "metadata": {
     "editable": true
    },
@@ -4190,7 +4190,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d8c0246",
+   "id": "3919a2cb",
    "metadata": {
     "editable": true
    },
@@ -4200,7 +4200,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f73a9f8b",
+   "id": "ddf99a3e",
    "metadata": {
     "editable": true
    },
@@ -4212,7 +4212,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ce5f423",
+   "id": "5a790d25",
    "metadata": {
     "editable": true
    },
@@ -4226,7 +4226,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3ec391cc",
+   "id": "113a5d16",
    "metadata": {
     "editable": true
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@@ -4238,7 +4238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11a3f35c",
+   "id": "ec65ec89",
    "metadata": {
     "editable": true
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@@ -4250,7 +4250,7 @@
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   {
    "cell_type": "markdown",
-   "id": "c6b8757c",
+   "id": "ed891134",
    "metadata": {
     "editable": true
    },
@@ -4260,7 +4260,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e2f4fc0",
+   "id": "5266f146",
    "metadata": {
     "editable": true
    },
@@ -4272,7 +4272,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db3e6c79",
+   "id": "666ab5b3",
    "metadata": {
     "editable": true
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@@ -4283,7 +4283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d95e8aa",
+   "id": "ab9a3eec",
    "metadata": {
     "editable": true
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@@ -4295,7 +4295,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7dfc330",
+   "id": "252e7533",
    "metadata": {
     "editable": true
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@@ -4305,7 +4305,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "888796de",
+   "id": "201b9300",
    "metadata": {
     "editable": true
    },
@@ -4317,7 +4317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99561aeb",
+   "id": "4f6287cf",
    "metadata": {
     "editable": true
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@@ -4327,7 +4327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a4556b6",
+   "id": "1ace6d06",
    "metadata": {
     "editable": true
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@@ -4339,7 +4339,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9844b480",
+   "id": "274f98fb",
    "metadata": {
     "editable": true
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@@ -4350,7 +4350,7 @@
   },
   {
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-   "id": "3731b9ff",
+   "id": "70dc1b76",
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@@ -4362,7 +4362,7 @@
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   {
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-   "id": "2debf83f",
+   "id": "096c55e9",
    "metadata": {
     "editable": true
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@@ -4380,7 +4380,7 @@
   },
   {
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-   "id": "7fd0c7b2",
+   "id": "0ac9bdae",
    "metadata": {
     "editable": true
    },
@@ -4396,19 +4396,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db45a990",
+   "id": "a456e251",
    "metadata": {
     "editable": true
    },
    "source": [
     "$$\n",
-    "\\frac{\\partial^2 C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}^T\\partial \\boldsymbol{\\beta}} =\\frac{2}{n}\\boldsymbol{X}^T\\boldsymbol{X}.\n",
+    "\\frac{\\partial^2 C(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} =\\frac{2}{n}\\boldsymbol{X}^T\\boldsymbol{X}.\n",
     "$$"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "476e4063",
+   "id": "7c817401",
    "metadata": {
     "editable": true
    },
@@ -4420,7 +4420,7 @@
   },
   {
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-   "id": "f7caedf0",
+   "id": "20d7bb5d",
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@@ -4432,7 +4432,7 @@
   },
   {
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-   "id": "a9469af7",
+   "id": "52a9f64e",
    "metadata": {
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@@ -4445,7 +4445,7 @@
   },
   {
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-   "id": "dae869bb",
+   "id": "77820e66",
    "metadata": {
     "editable": true
    },
@@ -4461,7 +4461,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d718bf56",
+   "id": "dc6ab9cd",
    "metadata": {
     "editable": true
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@@ -4475,7 +4475,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5ad97e4",
+   "id": "8a8ee502",
    "metadata": {
     "editable": true
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@@ -4485,7 +4485,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b76f1367",
+   "id": "f377b529",
    "metadata": {
     "editable": true
    },
@@ -4497,7 +4497,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc7b9319",
+   "id": "e572a54d",
    "metadata": {
     "editable": true
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@@ -4507,7 +4507,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8159fef4",
+   "id": "1b9c72f5",
    "metadata": {
     "editable": true
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@@ -4519,7 +4519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d34ac113",
+   "id": "15c56784",
    "metadata": {
     "editable": true
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@@ -4529,7 +4529,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e0b77c9",
+   "id": "a03c1a32",
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     "editable": true
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@@ -4543,7 +4543,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01cb77e3",
+   "id": "af372da2",
    "metadata": {
     "editable": true
    },
@@ -4554,13 +4554,13 @@
     "method corrects the bias in the estimation of the population variance\n",
     "and covariance. It also partially corrects the bias in the estimation\n",
     "of the population standard deviation. If you use a library like\n",
-    "**Scikit-Learn** or **nunmpy's** function calculate the covariance, this\n",
+    "**Scikit-Learn** or **nunmpy's** function to calculate the covariance, this\n",
     "quantity will be computed with a factor $1/(n-1)$."
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "e69ed735",
+   "id": "9200f285",
    "metadata": {
     "editable": true
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@@ -4576,7 +4576,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f0da7f4b",
+   "id": "d5becae6",
    "metadata": {
     "editable": true
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@@ -4588,7 +4588,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "935ca456",
+   "id": "27e6e5b8",
    "metadata": {
     "editable": true
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@@ -4601,7 +4601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06f10a4e",
+   "id": "06454f55",
    "metadata": {
     "editable": true
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@@ -4615,7 +4615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be61cd6a",
+   "id": "833b2511",
    "metadata": {
     "editable": true
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@@ -4625,7 +4625,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0e25f2ad",
+   "id": "056aceed",
    "metadata": {
     "editable": true
    },
@@ -4638,7 +4638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe5ccfec",
+   "id": "950f361e",
    "metadata": {
     "editable": true
    },
@@ -4657,7 +4657,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eefbdf95",
+   "id": "2d8ac5c2",
    "metadata": {
     "editable": true
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@@ -4669,7 +4669,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05b5b021",
+   "id": "62d04779",
    "metadata": {
     "editable": true
    },
@@ -4681,7 +4681,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17df2dd0",
+   "id": "797b13b8",
    "metadata": {
     "editable": true
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@@ -4691,7 +4691,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "286fc60b",
+   "id": "bd705147",
    "metadata": {
     "editable": true
    },
@@ -4703,7 +4703,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9918e3f5",
+   "id": "542850cc",
    "metadata": {
     "editable": true
    },
@@ -4716,7 +4716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11803309",
+   "id": "db1aaf48",
    "metadata": {
     "editable": true
    },
@@ -4735,7 +4735,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81195690",
+   "id": "6dc65433",
    "metadata": {
     "editable": true
    },
@@ -4745,7 +4745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a402445",
+   "id": "ccd95a67",
    "metadata": {
     "editable": true
    },
@@ -4764,7 +4764,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4c0f4547",
+   "id": "c15cc257",
    "metadata": {
     "editable": true
    },
@@ -4782,7 +4782,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "238844a1",
+   "id": "cc4a5463",
    "metadata": {
     "editable": true
    },
@@ -4796,7 +4796,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "33ddecf3",
+   "id": "b8cfd6fa",
    "metadata": {
     "editable": true
    },
@@ -4811,7 +4811,7 @@
   {
    "cell_type": "code",
    "execution_count": 27,
-   "id": "5b7e3d47",
+   "id": "31e1da88",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4832,7 +4832,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b5203c81",
+   "id": "24a933c2",
    "metadata": {
     "editable": true
    },
@@ -4849,7 +4849,7 @@
   {
    "cell_type": "code",
    "execution_count": 28,
-   "id": "6ca9fe2f",
+   "id": "8d9779ce",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4881,7 +4881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a33aee4",
+   "id": "c7e322b5",
    "metadata": {
     "editable": true
    },
@@ -4895,7 +4895,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be321ad7",
+   "id": "ea5682d7",
    "metadata": {
     "editable": true
    },
@@ -4908,7 +4908,7 @@
   {
    "cell_type": "code",
    "execution_count": 29,
-   "id": "df41b33a",
+   "id": "0e83fcbc",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -4933,7 +4933,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "37e53b7c",
+   "id": "1226fab9",
    "metadata": {
     "editable": true
    },
@@ -4943,7 +4943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "470d603b",
+   "id": "923ffc58",
    "metadata": {
     "editable": true
    },
@@ -4954,7 +4954,7 @@
   {
    "cell_type": "code",
    "execution_count": 30,
-   "id": "d15a64cf",
+   "id": "145c2622",
    "metadata": {
     "collapsed": false,
     "editable": true
@@ -5008,7 +5008,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "450109da",
+   "id": "8a657c92",
    "metadata": {
     "editable": true
    },
@@ -5025,7 +5025,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "15d78e68",
+   "id": "522f204b",
    "metadata": {
     "editable": true
    },
@@ -5037,7 +5037,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05d71468",
+   "id": "6ab032e5",
    "metadata": {
     "editable": true
    },
@@ -5049,7 +5049,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "579b77d0",
+   "id": "423a9a47",
    "metadata": {
     "editable": true
    },
@@ -5059,7 +5059,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b77d639",
+   "id": "817b323b",
    "metadata": {
     "editable": true
    },
@@ -5076,7 +5076,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6f64deb",
+   "id": "93f4ff8f",
    "metadata": {
     "editable": true
    },
@@ -5086,7 +5086,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6416bd42",
+   "id": "437c6704",
    "metadata": {
     "editable": true
    },
@@ -5101,7 +5101,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd76a3d6",
+   "id": "fe76cb03",
    "metadata": {
     "editable": true
    },
@@ -5111,7 +5111,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7667e919",
+   "id": "71d190a9",
    "metadata": {
     "editable": true
    },
@@ -5125,7 +5125,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a364fdec",
+   "id": "21d676ff",
    "metadata": {
     "editable": true
    },
@@ -5137,7 +5137,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e30f36d",
+   "id": "95bf7f81",
    "metadata": {
     "editable": true
    },
@@ -5149,7 +5149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a8706a80",
+   "id": "3e6fccbc",
    "metadata": {
     "editable": true
    },
@@ -5161,7 +5161,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9e7b5b3",
+   "id": "8c261002",
    "metadata": {
     "editable": true
    },
@@ -5171,7 +5171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58f9f374",
+   "id": "f9aedabd",
    "metadata": {
     "editable": true
    },
@@ -5183,7 +5183,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ccd3b380",
+   "id": "b9c3ddc5",
    "metadata": {
     "editable": true
    },
@@ -5193,7 +5193,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4febae0d",
+   "id": "ed30a2b1",
    "metadata": {
     "editable": true
    },
@@ -5210,7 +5210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5264a8ef",
+   "id": "dfb0eb4a",
    "metadata": {
     "editable": true
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@@ -5220,7 +5220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6306d337",
+   "id": "39664ac4",
    "metadata": {
     "editable": true
    },
@@ -5232,7 +5232,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0b85ad53",
+   "id": "36858bcd",
    "metadata": {
     "editable": true
    },
@@ -5242,7 +5242,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f462bd9",
+   "id": "1938dd21",
    "metadata": {
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@@ -5254,7 +5254,7 @@
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   {
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-   "id": "3e998d31",
+   "id": "d89b7fce",
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@@ -5268,7 +5268,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "93ad8f0c",
+   "id": "a30a69b4",
    "metadata": {
     "editable": true
    },
@@ -5280,7 +5280,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ec4e112e",
+   "id": "34639fb6",
    "metadata": {
     "editable": true
    },
@@ -5302,7 +5302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36422c93",
+   "id": "20ad8e3f",
    "metadata": {
     "editable": true
    },
@@ -5314,7 +5314,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c726caf1",
+   "id": "d9478bfc",
    "metadata": {
     "editable": true
    },
@@ -5329,7 +5329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13624ec5",
+   "id": "04d7397f",
    "metadata": {
     "editable": true
    },
@@ -5341,7 +5341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5f5dbbb",
+   "id": "59f21f2c",
    "metadata": {
     "editable": true
    },
@@ -5353,7 +5353,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5a06622",
+   "id": "a309e6d5",
    "metadata": {
     "editable": true
    },
@@ -5363,7 +5363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "472afc38",
+   "id": "2c4186ec",
    "metadata": {
     "editable": true
    },
@@ -5375,7 +5375,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "719c02f4",
+   "id": "ccd854d0",
    "metadata": {
     "editable": true
    },
@@ -5385,7 +5385,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b2a62207",
+   "id": "74eaeda4",
    "metadata": {
     "editable": true
    },
@@ -5397,7 +5397,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6194792e",
+   "id": "053b8482",
    "metadata": {
     "editable": true
    },
@@ -5407,7 +5407,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c957d867",
+   "id": "6f8a528a",
    "metadata": {
     "editable": true
    },
@@ -5419,7 +5419,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d0a4281",
+   "id": "112070df",
    "metadata": {
     "editable": true
    },
@@ -5436,7 +5436,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3a982382",
+   "id": "33e268b0",
    "metadata": {
     "editable": true
    },
@@ -5449,7 +5449,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9fa67077",
+   "id": "0de7adcd",
    "metadata": {
     "editable": true
    },
@@ -5461,7 +5461,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d70a4c10",
+   "id": "fa30d846",
    "metadata": {
     "editable": true
    },
@@ -5471,7 +5471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "61ce3a16",
+   "id": "d577ef22",
    "metadata": {
     "editable": true
    },
@@ -5484,7 +5484,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7110d4e",
+   "id": "ce39ce20",
    "metadata": {
     "editable": true
    },
@@ -5494,7 +5494,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "102fd8e6",
+   "id": "960bd21b",
    "metadata": {
     "editable": true
    },
@@ -5506,7 +5506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea3f1c3b",
+   "id": "7736561e",
    "metadata": {
     "editable": true
    },
@@ -5519,7 +5519,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e7d3edc",
+   "id": "f1043146",
    "metadata": {
     "editable": true
    },
@@ -5532,7 +5532,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6138e4d3",
+   "id": "56e791a2",
    "metadata": {
     "editable": true
    },
@@ -5544,7 +5544,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8406ec32",
+   "id": "dbcb265a",
    "metadata": {
     "editable": true
    },
@@ -5556,7 +5556,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8725c04e",
+   "id": "9e1a00c1",
    "metadata": {
     "editable": true
    },
@@ -5566,7 +5566,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dcb02b56",
+   "id": "6ca6c71d",
    "metadata": {
     "editable": true
    },
@@ -5579,7 +5579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fdc3d5dc",
+   "id": "797658d0",
    "metadata": {
     "editable": true
    },
@@ -5591,7 +5591,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a06957b",
+   "id": "ed64a13e",
    "metadata": {
     "editable": true
    },
@@ -5603,7 +5603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5d3c2482",
+   "id": "fc6a2aeb",
    "metadata": {
     "editable": true
    },
@@ -5615,7 +5615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e94ba1d9",
+   "id": "1c956ba4",
    "metadata": {
     "editable": true
    },
@@ -5627,7 +5627,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebee0c20",
+   "id": "ea5516df",
    "metadata": {
     "editable": true
    },
@@ -5641,7 +5641,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e30e7753",
+   "id": "b6d61e24",
    "metadata": {
     "editable": true
    },
@@ -5653,7 +5653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf0db09e",
+   "id": "84765a82",
    "metadata": {
     "editable": true
    },
@@ -5663,7 +5663,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "09c45e7a",
+   "id": "973019d8",
    "metadata": {
     "editable": true
    },
@@ -5675,7 +5675,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3691ef57",
+   "id": "7f074350",
    "metadata": {
     "editable": true
    },
@@ -5687,7 +5687,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86e182d9",
+   "id": "0570ceae",
    "metadata": {
     "editable": true
    },
@@ -5699,7 +5699,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb5f1b1c",
+   "id": "5d16ea9d",
    "metadata": {
     "editable": true
    },
@@ -5711,7 +5711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "64a361ad",
+   "id": "b739c33e",
    "metadata": {
     "editable": true
    },
@@ -5723,7 +5723,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "736ab040",
+   "id": "dc8bc23b",
    "metadata": {
     "editable": true
    },
@@ -5742,7 +5742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e5e13b7",
+   "id": "d89da6dc",
    "metadata": {
     "editable": true
    },
@@ -5754,7 +5754,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f5b34bc6",
+   "id": "3b871cb3",
    "metadata": {
     "editable": true
    },
@@ -5764,7 +5764,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "05fed0df",
+   "id": "018e1163",
    "metadata": {
     "editable": true
    },
@@ -5776,7 +5776,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0853969f",
+   "id": "24f364d8",
    "metadata": {
     "editable": true
    },
@@ -5786,7 +5786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e1e0e802",
+   "id": "4f695ec4",
    "metadata": {
     "editable": true
    },
@@ -5798,7 +5798,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5349338e",
+   "id": "a4599188",
    "metadata": {
     "editable": true
    },
@@ -5810,7 +5810,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3856bb34",
+   "id": "0edf0a0c",
    "metadata": {
     "editable": true
    },
@@ -5826,7 +5826,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "96bb9c00",
+   "id": "9afad20c",
    "metadata": {
     "editable": true
    },
@@ -5838,7 +5838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "343e7f2a",
+   "id": "33df2d17",
    "metadata": {
     "editable": true
    },
@@ -5850,7 +5850,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9a0dd13",
+   "id": "972e10e7",
    "metadata": {
     "editable": true
    },
@@ -5860,7 +5860,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "47f89929",
+   "id": "86f89bca",
    "metadata": {
     "editable": true
    },
@@ -5872,7 +5872,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6a8d40da",
+   "id": "c286d017",
    "metadata": {
     "editable": true
    },
@@ -5882,7 +5882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "87a36c85",
+   "id": "4dcbe7e5",
    "metadata": {
     "editable": true
    },
@@ -5894,7 +5894,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6237d1b0",
+   "id": "43db48d4",
    "metadata": {
     "editable": true
    },
@@ -5911,7 +5911,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39430adb",
+   "id": "17d8c95a",
    "metadata": {
     "editable": true
    },
@@ -5923,7 +5923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b97b5db8",
+   "id": "3c9d6593",
    "metadata": {
     "editable": true
    },
@@ -5935,7 +5935,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06fb16da",
+   "id": "a1606a04",
    "metadata": {
     "editable": true
    },
@@ -5945,7 +5945,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "552d08cd",
+   "id": "d192512a",
    "metadata": {
     "editable": true
    },
@@ -5957,7 +5957,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4e2d1b42",
+   "id": "a60675a1",
    "metadata": {
     "editable": true
    },
@@ -5967,7 +5967,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbc4cda5",
+   "id": "942fc37f",
    "metadata": {
     "editable": true
    },
@@ -5979,7 +5979,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e36f9245",
+   "id": "4f5e067f",
    "metadata": {
     "editable": true
    },
@@ -5989,7 +5989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06b74c95",
+   "id": "d330f743",
    "metadata": {
     "editable": true
    },
@@ -6001,7 +6001,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1cbd57d2",
+   "id": "55f9b635",
    "metadata": {
     "editable": true
    },
@@ -6011,7 +6011,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17a0dae2",
+   "id": "5a6d1b0b",
    "metadata": {
     "editable": true
    },
@@ -6023,7 +6023,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abc993af",
+   "id": "12fd13cb",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week35/week35.do.txt b/doc/src/week35/week35.do.txt
index 593617daa..12707253a 100644
--- a/doc/src/week35/week35.do.txt
+++ b/doc/src/week35/week35.do.txt
@@ -2132,7 +2132,7 @@ function, that is we have
 
 !bt
 \[
-\frac{\partial^2 C(\bm{\beta})}{\partial \bm{\beta}^T\partial \bm{\beta}} =\frac{2}{n}\bm{X}^T\bm{X}.  
+\frac{\partial^2 C(\bm{\beta})}{\partial \bm{\beta}\partial \bm{\beta}^T} =\frac{2}{n}\bm{X}^T\bm{X}.  
 \]
 !et
 This quantity defines was what is called the Hessian matrix (the second derivative of a function we want to optimize).
@@ -2194,7 +2194,7 @@ with a factor $1/(n-1)$. This is called "Bessel's correction":"https://mathworld
 method corrects the bias in the estimation of the population variance
 and covariance. It also partially corrects the bias in the estimation
 of the population standard deviation. If you use a library like
-_Scikit-Learn_ or _nunmpy's_ function calculate the covariance, this
+_Scikit-Learn_ or _nunmpy's_ function to calculate the covariance, this
 quantity will be computed with a factor $1/(n-1)$.
 
 !split